A solution to this problem, as known from the prior art, consists in forming a package body assembly which is arranged between semiconductor chips arranged in a matrix. The package body assembly may, for example, be produced using a casting method. In a subsequent method step, the package body assembly is singulated into a multiplicity of optoelectronic semiconductor devices, such that each singulated semiconductor device comprises at least one semiconductor chip and one part of the package body assembly as package body. Furthermore, the semiconductor devices produced in this way often comprise conversion elements consisting of a wavelength-converting conversion material.